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Permutations of finite fields for check digit systems. (English) Zbl 1248.11100
From the authors’ abstract: Let $$q$$ be a prime power and $$n$$ a positive divisor of $$q-1$$. We prove an asymptotic formula for the number of polynomials $f(X)=\frac{a-b}{n}\bigg(\sum_{j=1}^{n-1} X^{j(q-1)/n}\bigg)X+\frac{a+b(n-1)}{n}\,X\in\mathbb{F}_q[X]$ such that the polynomials $$f(X)$$, $$f(X)\pm X$$, and $$f(f(X))\pm X$$ are all permutation polynomials over $$\mathbb{F}_q$$.

MSC:
 11T06 Polynomials over finite fields 11T22 Cyclotomy 11T71 Algebraic coding theory; cryptography (number-theoretic aspects)
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References:
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